The historical setting

The Ishango bone, discovered at the "Fisherman Settlement" of Ishango in the Democratic Republic of the Congo, is a bone tool and possible mathematical device that dates to the Upper Paleolithic era. The curved bone is dark brown in color, about 10 centimeters in length, and features a sharp piece of quartz affixed to one end, perhaps for engraving. Because the bone has been narrowed, scraped, polished, and engraved to a certain extent, it is no longer possible to determine what animal the bone belonged to, although it is assumed to have been a mammal. The ordered engravings have led many to speculate about the meaning behind these marks, including interpretations involving mathematical significance or astrological relevance.

It is thought by some to be a tally stick, as it features a series of marks that have been interpreted as tally marks carved in three columns running the length of the tool, although it has also been suggested that the scratches might have been to create a better grip on the handle or for some other non-mathematical reason.

Archaeological discovery

The Ishango bone was found in 1950 by Belgian Jean de Heinzelin de Braucourt while exploring what was then the Belgian Congo. It was discovered in the area of Ishango near the Semliki River. Lake Edward empties into the Semliki, which forms part of the headwaters of the Nile River (now on the border between modern-day Uganda and D.R. Congo). The Late Stone Age human remains from Ishango belong to Homo sapiens, although they exhibit some archaic morphological characteristics. The most recent inhabitants, who gave the area its name, have no immediate connections with the primary settlement, which was "buried in a volcanic eruption".

On an excavation, de Heinzelin discovered a bone about the "size of a pencil" amongst human remains and many stone tools in a small community that fished and gathered in this area of Africa. Professor de Heinzelin brought the Ishango bone to Belgium, where it was stored in the treasure room of the Royal Belgian Institute of Natural Sciences in Brussels. Several molds and copies were created from the petrified bone in order to preserve the delicate nature of the fragile artifact while being exported. A written request to the museum was required to see the artifact, as it was no longer on public display.

Mathematical

The 168 etchings on the bone are ordered in three parallel columns along the length of the bone, with each mark having a varying orientation and length. The first column, or central column along the most curved side of the bone, is referred to as the M column, from the French word milieu (middle). The left and right columns are respectively referred to as G and D, or gauche (left) and droite (right) in French. The parallel markings have led to various hypotheses, such as that the implement indicates an understanding of decimals or prime numbers.

Though these propositions have been questioned, it is considered likely by many scholars that the tool was used for mathematical purposes, perhaps including simple mathematical procedures or to construct a numeral system. The discoverer of the Ishango bone, de Heinzelin, suggested that the bone was evidence of knowledge of simple arithmetic, or at least that the markings were "deliberately planned". He based his interpretation on archaeological evidence, comparing "Ishango harpoon heads to those found in northern Sudan and ancient Egypt".

This comparison led to the suggestion of a link between arithmetic processes conducted at Ishango with the "commencement of mathematics in ancient Egypt." The third column has been interpreted as a "table of prime numbers", as column G appears to illustrate prime numbers between 10 and 20, but this might be a coincidence.

Astronomical

Alexander Marshack, an archaeologist from Harvard University, speculated that the Ishango bone represents numeric notation of a six-month lunar calendar after conducting a "detailed microscopic examination" of the bone. This idea arose from the fact that the markings on the first two columns add up to 60, corresponding with two lunar months, and the sum of the number of carvings on the last row being 48, or a month and a half. Marshack generated a diagram comparing the different sizes and phases of the Moon with the notches of the Ishango bone. There is some circumstantial evidence to support this alternate hypothesis, being that present day African societies utilize bones, strings, and other devices as calendars.

Critics in the field of archaeology have concluded, however, that Marshack's interpretation is flawed and describe that his analysis of the Ishango bone confines itself to a simple search for a pattern, rather than an actual test of his hypothesis. This has also led Claudia Zaslavsky to suggest that the creator of the tool could have been a woman, tracking the lunar phase in relation to the menstrual cycle.